Carbon dioxide capture, EOR utilization, and storage (CCUS-EOR) reduce emissions while enhancing oil recovery, with Water-Alternating-Gas (WAG) flooding as a key technology. However, WAG performance is constrained by gas properties, notably gravitational override. Existing quantitative override indices mostly apply to homogeneous reservoirs and gas flooding, leaving challenges in evaluating override during WAG in highly heterogeneous carbonate rocks. This study develops a quantitative index to characterize override degree in heterogeneous reservoirs under WAG, for numerical simulation analysis. It uses the gas-unswept area proportion for homogeneous reservoirs and defines an override weight and a judgment coefficient for heterogeneous ones. Reservoir models with varied vertical heterogeneities and well-rates were built to analyze parameter impacts on override degree and the impact of override on recovery efficiency via this index. Results show the index accurately characterizes gas override in heterogeneous reservoirs during WAG simulations. Dominance of gravity or permeability contrast causes poor gas sweep and premature breakthrough, but these two factors can counterbalance under certain conditions, improving sweep efficiency and recovery. Findings aid understanding of gas sweep patterns in WAG of thick carbonate reservoirs, providing a theoretical basis for field adjustments.

Water injection is the most important energy-supplement method worldwide for sandstone and carbonate reservoirs after depletion development, and the rational and efficient development of waterflooding reservoirs is crucial. Owing to reservoir heterogeneity, such as high-permeability streaks and faults, waterflooding reservoirs often face difficulties in the middle and late stages of development, including low sweep efficiency, low recovery degree, and limited means for injection-production adjustment. To restrain production decline, control the rise of water cut, and maintain reservoir pressure, it is urgently necessary to develop fast, stable, and reliable production optimization methods. Based on the injection-production allocation relationship obtained from streamline simulation, this paper defines injection/production efficiencies at the well-pair and single-well levels and combines them with a rate optimization strategy, including rate updating criteria and updating modes. A streamline-based well-control optimization method based on injection/production efficiency is proposed. This streamline optimization method is simple and efficient and is insensitive to the numbers of injection and production wells. By combining an initial experimental design method, surrogate models, and sampling strategies—including three strategies, namely “minimum surrogate response,” “maximum search ability,” and “maximum integrated value,” as well as two approaches for seeking “potential candidate points”, namely screening feasible points and optimization-based solution—a new surrogate optimization algorithm suitable for time-consuming constrained optimization is proposed. By running the aforementioned streamline optimization procedure within the surrogate optimization framework, a streamline-based surrogate optimization algorithm is derived. The reliability of the proposed method is verified using two numerical examples. The results show that the optimized schedules achieve obvious oil-increasing and water-controlling effects and significantly improve economic benefits. The streamline-based surrogate optimization algorithm integrates the advantages of individual methods, overcomes the applicability limitation that the streamline method is mainly suitable for well-control optimization, and avoids the time-consuming problem caused by a pure surrogate optimization method when handling large-scale production optimization. In the future, it can also be applied to joint optimization of well patterns, well locations, and well-control parameters.

Waterflooding, the predominant secondary recovery method in global sandstone and carbonate reservoirs, faces challenges including premature water breakthroughs, rapid water cut rise, limited well pattern adjustments and restricted stimulation treatments due to complex geological constraints. This demands enhanced optimization techniques. Leveraging streamline simulation’s flow diagnostic capabilities, this study introduces two novel metrics: “real-time streamline revenue” (RTSR), quantifying the economic effectiveness via flux, time of flight and saturation data integration along streamlines, and “well-pair revenue efficiency” for injection-production unit characterization. Integrating corresponding rate optimization criteria, we develop an RTSR-based production optimization methodology which enables rapid generation of optimal injection-production schedules, improving recovery while controlling water production. Validation using synthetic and field-scale models (Reservoir M) demonstrated significant improvements by the proposed method: Synthetic case achieved 29.42% NPV increase, 26.88% oil production rise, and 8.60% water reduction compared to the base schedule; Reservoir M yielded 20.80% higher NPV, 20.41% more oil, and 72.69% less water. The approach outperforms existing streamline methods, proving effective for stabilizing/enhancing oil production and reducing water cut. Future work can refine weighting functions within optimization criteria using surrogate-optimization algorithms and extend the framework to integrate layer series, well patterns, or well placement with injection-production control.

The accurate prediction of the minimum miscibility pressure (MMP) for sour natural gas—reservoir oil is of paramount importance for the design and optimization of gas injection processes, particularly in enhanced oil recovery (EOR) and gas cycling schemes. This study introduces intelligent models that leverages machine learning algorithms to predict the MMP between reservoir oil and injected sour natural gas. The model is trained and validated using a comprehensive dataset encompassing various oil properties, reservoir temperature, and gas compositions commonly encountered in sour natural gas. The different machine learning methods are chosen to construct the MMP forecasting model with influential parameters affecting MMP, followed by the comparison of predictive accuracy of different approaches. Validation results demonstrate that the intelligent model achieves great predicting effects. The superior performance of model is attributed to its ability to capture intricate patterns and interactions within the dataset that are often overlooked by conventional methods. Furthermore, the intelligent model offers a user-friendly interface for rapid MMP prediction, enabling petroleum engineers to make informed decisions regarding gas injection strategies without the need for extensive laboratory experiments or complex simulations. This not only enhances operational efficiency but also contributes to cost savings and risk reduction in the development under the sour natural gas injection condition. In conclusion, the integration of machine learning techniques and comprehensive datasets provides a robust and accurate tool for the petroleum industry, facilitating the optimization of gas injection processes and thus enhancement of oil recovery from challenging reservoirs.

The bottomhole pressure is one of the key parameters for oilfield development and decision-making. However, due to factors such as cost and equipment failure, bottomhole pressure data is often lacking. In this paper, we established a GA-XGBoost model to predict the bottomhole pressure in carbonate reservoirs. Firstly, a total of 413 datasets, including daily oil production, daily water production, daily gas production, daily liquid production, daily gas injection rate, gas–oil ratio, and bottomhole pressure, were collected from 14 wells through numerical simulation. The production data were then subjected to standardized preprocessing and dimensionality reduction using a principal component analysis. The data were then split into training, testing, and validation sets with a ratio of 7:2:1. A prediction model for the bottomhole pressure in carbonate reservoirs based on XGBoost was developed. The model parameters were optimized using a genetic algorithm, and the average adjusted R-squared score from the cross-validation was used as the optimization metric. The model achieved an adjusted R-squared score of 0.99 and a root-mean-square error of 0.0015 on the training set, an adjusted R-squared score of 0.84 and a root-mean-square error of 0.0564 on the testing set, and an adjusted R-squared score of 0.69 and a root-mean-square error of 0.0721 on the validation set. The results demonstrated that in the case of fewer data variables, the GA-XGBoost model had a high accuracy and good generalization performance, and its performance was superior to other models. Through this method, it is possible to quickly predict the bottomhole pressure data of carbonate rocks while saving measurement costs.

Abstract The rapid and accurate forecasting of performance in the Steam-Assisted Gravity Drainage (SAGD) process for oil sands is crucial for the reasonable design of the development plan. This study aims to address this need by presenting novel data-driven performance indicators based on support vector regression (SVR), a machine learning method that complements the traditional physics-driven approach. During the SAGD process, steam is injected into the reservoir to heat the bitumen, reducing its viscosity, and allowing it to flow towards a lower well where it can be collected. The performance of the SAGD process depends on various factors such as steam injection rate, reservoir heterogeneity, and operating conditions. Accurately forecasting the performance of the SAGD process can help optimize these parameters and improve the overall efficiency of oil sands recovery. The data-driven performance indicators proposed in this study utilize the SVR method to establish a relationship between input parameters and the desired performance outputs. In the constructing process, some parameter optimization algorithms, like grid search method, particle swarm optimization algorithm and genetic algorithm, are used to identify the optimal SVR model structure. The validation results show that the design meets the desired objectives. All in all, through proposed data-driven performance indicators, the performance of SAGD process in candidate oil sands projects could be rapidly and easily obtained.

In the development process of thick reservoirs, the impact of various geological factors on the effectiveness of the CO2 water alternating gas (CO2-WAG) flooding technology remains unclear. This paper establishes multiple CO2-WAG flooding models for thick reservoirs to study the effects of sedimentary rhythm, dip angle, matrix permeability, high-permeability streaks (HPS), and barrier layers on the effectiveness of CO2-WAG flooding and then uses the random forest algorithm to rank the importance of these geological factors. The results show that different geological factors have varying degrees of impact on the distribution of water and gas migration and recovery rates during the CO2-WAG flooding process. The ranking of the importance of various factors obtained by reservoir numerical simulations and the random forest algorithm is HPS, sedimentary rhythm, dip angle, matrix permeability, and barrier layers. These research findings will provide effective guidance and a reference for the optimal selection of CO2-WAG flooding schemes for similar thick reservoirs under different geological conditions.

Abstract A deep-water offshore oil field belongs to a carbonate reservoir with a depth of over 2000 meters, and is developed using large well spacing water gas alternating (WAG) flooding. Compared with onshore oilfields, single well investment in deepwater oilfields is high, and in order to achieve the goal of high production with thin wells, the requirements for well location deployment are higher. At the same time, the presence of heterogeneity in carbonate reservoirs further increases the difficulty of well layout. Therefore, optimizing the well location for the development of water gas alternative flooding in deep water carbonate reservoirs to achieve optimal cumulative production and economic benefits is a challenge. Optimization of well locations based on numerical simulation usually requires engineers to spend a lot of time and energy. With the rapid development of artificial intelligence (AI) technology, using machine learning algorithms to optimize well locations may be a fast and reliable solution. The research started with data processing. Firstly, data related to well location optimization parameters are collected and pre-processed, such as data filling and data normalization. Pearson algorithm is used to judge the importance of feature parameters according to correlation, and finally the interference between features is reduced by dimensionality reduction algorithm. After data processing, a reservoir agent model is established based on XGBoost (eXtreme Gradient Boosting), the Sparrow Search Algorithm (SSA) is used to optimize the hyperparameters of the model, and SSA-XGBoost is used to optimize the well location of deepwater carbonate reservoirs in multiple rounds. The results clearly show that AI is a powerful tool for optimizing well placement in deepwater carbonate reservoirs. SSA-XGBoost model scored 0.99 in the training set decision coefficient, 0.96 in the test set decision coefficient, and 0.83 in the verification set decision coefficient, which has higher prediction accuracy compared with other machine learning algorithms. This study provides a technical method for the location optimization of WAG flooding Wells in deep water carbonate reservoirs

Nowadays, the steam conformance analysis and vapor-liquid interface (liquid pool level) of the typical horizontal well in SAGD operation is relatively mature. With the advancement of technology, some of multi-lateral horizontal wells engage in SAGD operation. However, steam conformance and liquid pool description, especially the lateral section is still one of the main difficulties. In this study, based on the modification of steam conformance formula, the judgment method of main horizontal and different types of multi-lateral wells is established. Meanwhile, the liquid pool of different types of multi-lateral wells is characterized by using the steam conformance. The research will provide technical support for the production improvement in multi-lateral horizontal wells in SAGD operation.

Under certain conditions, when crude oil is moved by external forces, the property of internal friction generated between crude oil molecules is called crude oil viscosity. The viscosity of crude oil reflects its complex seepage state in porous media. Underground crude oil with high viscosity, always has great flow resistance in porous media, thus the flowing becomes more difficult. Oil viscosity is an indispensable key parameter in the process of dynamic analysis, reservoir engineering calculation and reservoir numerical simulation, which has critical influence on the field of well production or crude oil storage and transportation. Due to different oil viscosity, recovery approach of oil reservoirs, technical measures for storage and transportation, and the quality of oil products will be affected. The composition of crude oil is complicated, but it is mainly composed of carbon and hydrogen elements. The composition has a crucial effect on oil viscosity. Therefore, according to composition data of the actual oil sample, the determination dataset of oil viscosity is constructed together with other key parameters that affect the viscosity of crude oil within the reservoirs. Based on various machine learning algorithms, like extremely randomized trees and XGBoost, determination methods of oil viscosity based on component data and machine learning algorithms are established. In the construction process of computational model of oil viscosity, whole dataset is parted to the training dataset and the testing dataset in the ratio of 8:2. The training dataset is mainly used to determine the best hyper-parameter combination of machine learning algorithm, while the testing dataset is used to determine the accuracy and adaptability of the corresponding method. Compared with methods such as experimental method and empirical formula method, the determination method of oil viscosity based on component data and machine learning algorithm does not require extra experimental costs and has a considerable degree of accuracy. Once the relevant input parameters are determined, the viscosity determination of multiple groups of oil samples could be completed quickly and accurately.

Block M is located in the eastern of the Orinoco Oil Belt in Venezuela. This block is a foamy extra-heavy oil reservoir. The average thickness of the main reservoir is 65–85 ft, the reservoir is 2906 ft deep, the original formation pressure is 1247 psi, the original dissolved gas oil ratio is 90 Scf/Stb, the underground oil viscosity is 3000 mPa · s, and the long horizontal well is adopted for cold production. Cold production productivity evaluation of horizontal wells for extra-heavy oil is of great significance for reservoir development and management. At present, many productivity evaluation models of horizontal wells are studied for conventional reservoirs. Therefore, this paper carried out the adaptability research of cold production productivity model of extra-heavy oil exploited by horizontal wells. The actual model of the single well is established by selecting typical horizontal wells and the history match is carried out. The productivity of horizontal wells with different horizontal section lengths is calculated by Borisov model, Joshi model, Giger model and Furui model respectively. The results are compared with those calculated by numerical model. It is found that Borisov model, Joshi model and Giger model for short horizontal section can not be used for the calculation of horizontal well productivity with long horizontal section. The Giger model applicable for long horizontal section and Furui model have a large error in calculating the horizontal well productivity with shorter horizontal section. These two models are suitable for horizontal well productivity in long horizontal well section. By analyzing the adaptability of different horizontal well productivity models, the paper provides supports for the evaluation of productivity and the optimization of next development.

In the SAGD process, steam is injected into the formation by the upper horizontal well, in order to warm the cold heavy oil and lower the oil viscosity within formation. Under the effect of gravity segregation, the heated oil flows to the lower horizontal well. Steam replaces the formation fluid, and accumulates to form a steam chamber. The shape and volume of the steam chamber is one of key parameters to understand the production performance of SAGD process. Nowadays, the widely used methods are reservoir simulation, mini-seismic and pressure-temperature profile in SAGD process, in order to monitor the development of steam chambers. Reservoir simulation is generally time-consuming and the results always depend on the accuracy of the input parameters. And also, only the overall size of the steam chamber can be obtained through the pressure/temperature well testing method, while the specific shape of the steam chamber cannot be identified. Furthermore, the mini-seismic monitoring results are accurate, but the cost is high, and real-time monitoring of the steam chamber cannot be achieved. In this paper, in order to understand the real-time development of the steam chamber, based on the field data, the temperature data of the observation well and the geological data are used for comprehensive analysis, and the development shape and volume of the steam chamber is evaluated in real time according to the material balance and heat conduction principal, and the three-dimensional description of the steam chamber is carried out.

The relative permeability curve reflects the relationship between the relative permeability of one phase and its saturation. The so-called relative permeability is the ratio of the effective permeability of a phase to the absolute permeability of the reservoir when multiphase fluids coexist and flow in the reservoir, and it reflects the relative mobility of each phase when they flow in porous media. In this paper, the research target is oil-water two-phase relative permeability curve. It is the basis for the study of oil-water two-phase seepage. It can comprehensively reflect the characteristics of oil-water two-phase seepage process and reservoir properties. And it is an indispensable and important parameter for calculating relative data of oilfield development, conducting dynamic analysis and reservoir numerical simulation. It also can be used in the process of history fitting and subsequent development scheme prediction, and it can guide the on-site operation in the actual production scenarios. In this paper, the overall dataset of relative permeability curve is constructed by using the data point of actual relative permeability curve. Based on the supervised machine learning theories, such as deep neural network and support vector regression machine, nine key factors, such as porosity, absolute permeability, initial water saturation, wettability and crude oil viscosity are taken as input features, while the relative permeability of oil phase and water phase are taken as output results. Several machine learning based prediction models of oil-water relative permeability curve are established. In the process of constructing the prediction model of oil-water relative permeability curve, the overall dataset is divided into training dataset, validation dataset and testing dataset in the proportion of 8:1:1. The validation dataset is mainly used to determine the best model structure, while the testing dataset is used to verify the accuracy and adaptability of the prediction model. Taking the accuracy indexes, which name is coefficient of determination, as the standard, the prediction model with the highest accuracy is determined by comparing the forecasting results of each prediction model. Especially the high accuracy of deep neural network model in the testing dataset proves that the model has strong adaptability and generalization ability. The prediction method of oil-water relative permeability curve which is based on deep neural network theory has its unique advantages. Importantly, expensive costs and long testing times are avoided, and it can complete the fast and accurate forecasting process of oil-water relative permeability, once the relevant parameters are inputted.

In order to improve the production performance of heavy oil reservoirs and clarify multiple flooding mechanisms, such as heating and extraction of pure solvent, based on the M Block in Canada, experiment of thermal solvent-assisted gravity drainage was carried out through two-dimensional physical simulation device, and the recovery mechanism of the thermal solvent-assisted gravity drainage under different pressures and temperatures was studied. The research results show that the hot solvent has the effect of heating and viscosity reduction, and the gaseous hot solvent has a certain latent heat of vaporization. When the gaseous hot solvent contacts the crude oil with a lower temperature, it will release heat to heat the crude oil and reduce the viscosity of the crude oil. The hot solvent has the characteristics of dissolving, extracting and reducing viscosity. Through de-asphalting, it can increase the content of light components and improve the properties of the product oil. The hot solvent has the effect of enhancing the diffusion, and the gaseous hot solvent has a larger molecular kinetic energy, and the swept range is larger than that of the liquid solvent. The lower interfacial tension between the solvent and the crude oil improves the oil sweep efficiency during the displacement process. Using the solvent-assisted gravity drainage method, the recovery factor can reach more than 60

The estimation of gas reserves or gas in place (GIP) is an important research area of oil and gas field development. It is significant to determine economically and effectively GIP for development planning and performance analysis of gas reservoirs. Therefore, based on the theory of gas flow through porous media and the introduction of two pseudo-variables (pseudo-pressure and pseudo-time functions), the method of separation of variables is innovatively employed to solve the mathematical model of gas flow. The resulting variable-rate solution is combined with the static material balance equation of gas reservoirs, then an iterative method for GIP calculation from production data and fluid properties is presented in this paper. Several numerical simulation cases and a field example prove the method applicable and reliable for various production systems. The calculation error of gas reserves is generally less than 5

The steam-assisted gravity drainage (SAGD) process is widely used for heavy oil and oil sands development, and has achieved large-scale commercial applications in Canada, China and other places. Since the main driving force in the SAGD operation is gravity, this puts forward higher requirements on the vertical distribution of the mud layer interval. In order to analyze the impact of centimeter-level laminate on the development of SAGD steam chamber development effect, this paper takes a Canadian oil field as the research object by using the key reservoir properties, with the help of reservoir simulation to carry out a variety of complex laminate distribution patterns. In the process of establishing the numerical model, the homogeneous static model is used as the basic research object, and the centimeter-level muddy laminate is determined by considering the different extension length, spacing. The influence of layers in different distribution modes on the development speed of steam chambers in different development stages, and also analysis of the key factors of centimeter-level mud laminate that affect the SAGD production performance in order to pro-vide certain support for new well deployment.

为建立一套海上砂岩油藏定向井初期产能的预测方法,综合考虑地质、工程与开发3个方面17项初期产能的影响因素,基于45口海上砂岩油藏定向井的2700组数据,组合使用Spearman相关系数、随机森林与递归特征消除算法对影响因素进行重要性排序;并结合油藏工程逻辑判别,筛选初期产能的主控因素.选用极端梯度提升(XG-Boost)算法构建初期产能预测模型,并基于产能公式改进其损失函数,增强数据挖掘算法的物理约束.结果表明:地层流动系数、孔隙度、层间地层流动系数变异系数、电潜泵下入垂深、储层射开厚度、井眼尺寸、生产压差、电潜泵频率以及油嘴尺寸是海上砂岩油藏定向井初期产能的主控因素.采用物理约束的XGBoost算法对5口井初期产能预测的平均相对误差为9.68％,而无物理约束的XGBoost算法预测初期产能的平均相对误差为11.68％.因此,物理约束可有效提升XGBoost算法对初期产能的预测精度,同时可实现海上砂岩油藏定向井初期产能的准确预测.

Z-factor, plays a significant role in the field of calculation research and engineering application including the calculation of PVT parameters, the research of oil & gas reservoir engineering, the design of surface pipeline, and so forth. It is necessary to find an effective approach to calculate the Z-factor quickly and precisely. This paper presents/develops a series of calculation models based on various supervised machine learning methods, such as support vector regression machine and extremely randomized trees, using 7148 data points of Z-factor. Pseudoreduced pressure (Ppr), pseudoreduced temperature (Tpr) and the ratio of Ppr to Tpr, are used as input features, while the value of Z-factor serves as output parameter. During the establishment process of calculation models, the Z-factor datasets are categorized into two: training dataset and testing dataset. Grid search method is adopted in different models, in order to find the optimal structure of the model. Calculation results obtained were evaluated using statistical indices: the average absolute percentage error (AAPE). A comparative research indicates that accuracy of the model based on extremely randomized trees is higher than other models, like support vector regression machine and BP neural network. The calculation results of the model based on extremely randomized trees are also compared with those calculated by other classic methods simultaneously, like DAK and DPR methods proposed by previous scholars. Results show that the model based on extremely randomized trees shows a better calculation performance. Compared with DAK and other calculation methods, the Z-factor calculation model of natural gas based on extremely randomized trees has its own advantage which could reduce the complexity caused by zonal calculation. Through proposed calculation model, the Z-factor of natural gas could be rapidly and precisely calculated, once a few parameters are inputted.

This work aims at the exploration of production data analysis (PDA) methods without iterations. It can overcome limitations of the advanced type curve analysis relying on the iterative calculation of material-balance pseudotime and current explicit methods reckoning on specific production schedule assumptions. The dynamic material balance equation (DMBE) is strictly proved by the integral variable substitution based on the gas flow equation under the boundary dominated flow (BDF) condition and the static material balance equation (SMBE) of a gas reservoir. We introduce the pseudopressure level function γ ( p ) and the recovery factor function R ( p ) to rewrite the DMBE in terms of observed variable Y and estimated variable Y e ; then the PDA can be transformed into an optimization problem of minimizing the error between Y and Y e . An optimization-based method for the explicit production data analysis of gas wells (OBM-EPDA), therefore, is developed in the paper, capable of determining the BDF constant and gas reserves explicitly and accurately for variable rate and/or variable flowing pressure systems. Three stimulated cases demonstrate the applicability and validity of OBM-EPDA with small errors less than 1% for estimated values of both reserves and Y . Not second to previous studies, the field case analysis further proves its practicability. It is shown that the nonlinear relation of γ to R can be represented by a polynomial function merely dependent on the inherent properties of the gas production system even before sorting out the production data. The errors of observed variable Y provided by OBM-EPDA facilitate the data quality control, and the elimination of outliers not subject to the BDF condition improves the reliability of the analysis. For various gas systems producing whether at a constant rate, a constant bottomhole pressure (BHP), or under variable rate and variable BHP conditions, the proposed method gives insights into the well-controlled volume and production capacity of the gas well whether in a low-pressure or high-pressure gas reservoir, where the compressibilities of rock and bound water are considered.

It is highly significant to determine precisely and rapidly the compressibility factor (Z-factor) of natural gases, a commonly used parameter in many engineering calculations concerning oil and gas reservoir development, such as material balance analysis, estimation of oil/gas in place, gas flow theory, numerical reservoir simulation, pipeline design and so on. A new Z-factor correlation, based on the Bender E (1970) equation of state and corresponding state principle, is developed in this paper, and then a new method for estimating gas compressibility factors continuously is proposed with the nonlinear regression analysis technique. The calculated results of DPR, HY, DAK correlations, commonly used in oil and gas reservoir engineering at present, are compared with those of the new method presented here, using standard data of Z-factor modified by the paper. The results of comparative analysis, based on isotherm error statistics and error distribution maps, show that the new method boasts a wider scope of application and a smoother error distribution. For the standard data points of Z-factor within the general pressure-temperature range (i.e., 0.2 ≤ ppr ≤ 15 & 1.05 ≤ Tpr ≤ 3.0) and relatively high-temperature & high-pressure range (i.e., 15 ≤ ppr ≤ 30 & 1.4 ≤ Tpr ≤ 2.8), its average absolute error (AAE) is 0.305% and 0.065% respectively, distinctly superior to the above three methods. Those approaches for determining gas compressibility factors based on correlations avoid the shortcomings of experimental measurements and type curves which are inefficient, time-consuming, and incapable of continuous estimations. Thus, the new method is recommended to determine Z-factor. The pseudo-critical parameters (i.e., ppc & Tpc) should be corrected beforehand in the presence of non-negligible non-hydrocarbon impurities in the gas mixture. The new method for calculating gas compressibility factors based on Bender (1970) equation of state can estimate the Z value quickly, accurately, and continuously under various pressure and temperature conditions through a simple iteration procedure, helpful to provide valuable reference for relevant engineering applications by virtue of its desirable calculation accuracy.